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Disentangling the Kaonic-Hydrogen Kfβ-Complex with DEAR

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Disentangling the Kaonic-Hydrogen Kfβ-Complex with DEAR IL NUOVO CIMENTOVOL. 110 A, N. 11 Novembre 1997 Disentangling the kaonic-hydrogen KFb-complex with DEAR 1 1 2 1 2 C. GUARALDO ( ), M. BRAGADIREANU ( )( ), M. ILIESCU ( )( ) 1 1 2 2 V. LUCHERINI ( ), C. PETRASCU ( )( ) and T. PONTA ( ) (1) INFN, Laboratori Nazionali di Frascati - C.P. 13, I-00044 Frascati (Roma), Italy (2) IFIN-HH - Bucharest-Magurele, P.O. Box MG6, R-76900 Romania (ricevuto il 12 Settembre 1997; approvato l’8 Ottobre 1997) Summary. — The possibility of disentangling for the first time the KFb-complex in kaonic hydrogen is shown to be realistic with the DEAR experiment. A precise identification of the pattern of lines in kaonic hydrogen and in kaonic deuterium can allow to obtain the first experimental determination of the KN sigma terms. PACS 13.75.Jz – Kaon-baryon interactions. PACS 36.10 – Exotic atoms and molecules (containing mesons, muons, and other unusual particles). 1. – Kaonic-hydrogen formation and energy levels An “exotic atom” is formed whenever an electron of an outer orbit of an atom is replaced by a heavier charged particle, such as a muon (m 2), or hadrons like a pion (p 2 ), a kaon (K2 ), an antiproton (p) or a sigma hyperon (S2 ). Among the exotic atoms, the hydrogen-like systems are of particular importance, because they have the simplest structure and are free from any screening effect due to bound electrons. By studying them, one can, for instance, directly probe the hadron-nucleon interaction at zero energy. The case of kaonic hydrogen. The mechanism of formation of a kaonic hydrogen atom is the following: a negative kaon enters into a hydrogen target; it loses its kinetic energy by ionization and excitation of the hydrogen molecules until it is captured into an atomic orbit around the proton (by replacing the electron). The capture orbit has the principal quantum number C C 2 ncapt km/me 25 (m and me are the reduced mass of the K p system and the electron mass, respectively), the Bohr radius of the kaonic system corresponding to that of the hydrogen K-shell electrons. Then the kaon cascades down through the series of atomic levels. The processes co-participating in the de-excitation of kaonic hydrogen are: 2 1 K 2 1 1 1) Molecular dissociation: ( K p )i H2 ( K p )f H H, which occurs when 4 2 D DEif Ei Ef 4.7 eV (dissociation energy of H2 molecule). G Società Italiana di Fisica 1347 1348 C. GUARALDO, M. BRAGADIREANU, M. ILIESCU, ETC. 2 1 K 2 1 1 1 2 2) External Auger transition: (K p )i H ( K p )f H e , which occurs D when DEif 15.6 eV (ionization energy of the H atom). 2 K 2 1 3) Radiative transition: (K p )i ( K p )f g. 4) Nuclear absorption, which is due to strong interaction and has a rate going as 1/n3. 5) Stark mixing: the strong electric field of the protons causes a mixing between degenerate states with the same principal quantum number and different angular momenta, the consequence being a nuclear absorption from high n states, preventing the kaon from reaching low-lying states. The effect is relevant in liquid hydrogen, where the high density gives high electrical fields. 6) Weak decay: the lifetime of the kaon plays a role for a dilute gas target. K The X-rays emitted in transitions to the 1s state constitute the K-series (Ka : 2p K K 1s; Kb : 3p 1s; Kg : 4p 1s; etc.), while the X-rays associated with transitions to the K K 2p state give the L-series (La : 3d 2p; Lb : 4d 2p; etc.). The energy levels of kaonic hydrogen can be calculated by solving the Klein-Gordon TABLE I. – Calculated energy levels of kaonic hydrogen. The solutions of the Klein-Gordon equation are given. The error on the kaon mass reflects in an uncertainty, given in parenthesis, of the 1s energy level. The uncertainty due to the unknown kaon charge distribution affects the evaluation of the finite size effect and is also given in parenthesis. As a consequence, the transition energies corresponding to the K-series lines are affected by an uncertainty of 1 eV. State Total Non- Vacuum Relativistic Finite-size Higher-order energy relativistic polarization correction effect vacuum (keV) energy (keV) (keV) (keV) polarization (keV) (keV) 1s 8.6339 8.6128 1 0.0219 1 0.0006 2 0.0016 1 0.0002 (6 0.0003) (60.0006) 2p 2.1542 2.1532 1 0.0008 1 0.0002 — — 3p 0.9573 0.9570 1 0.0002 1 0.0001 — — 4p 0.5384 0.5383 1 0.0001 — — — 5p 0.3445 0.3445 ———— 6p0.2393 0.2393 ———— 7p0.1758 0.1758 ———— 8p0.1346 0.1346 ———— Transition X-ray line Energy (keV) K 6 2p 1sKa 6.480 0.001 K 6 3p 1sKb 7.677 0.001 K 6 4p 1sKg 8.096 0.001 K 6 5p 1sKd 8.289 0.001 K 6 6p 1sKe 8.395 0.001 K 6 7p 1sKz 8.458 0.001 K 6 8p 1sKh 8.499 0.001 QK1sKQ 8.634 6 0.001 DISENTANGLING THE KAONIC-HYDROGEN KFb-COMPLEX WITH DEAR 1349 equation and taking into account: relativistic corrections, vacuum polarization and finite-size effects. They are tabulated in table I. The energy levels can be evaluated with the precision of the tenth of eV (see table). However, the error on the kaon mass and the unknown charge distribution of the kaon turn out in an overall numerical uncertainty on the energy of the 1s state of the order of one eV and of about few tenths of eV for the excited states. Consequently, the electromagnetic transition energies have an intrinsical uncertainty of 1 eV, as reported in table I. When the kaon reaches a state with a small angular momentum, state in which the overlap between the kaon and proton wavefunctions is large, the kaon is absorbed by the proton due to strong interaction. The strong interaction causes a shift of the low-lying levels from their pure electromagnetic positions, while the widths are increased. Shift and broadening are appreciable only in the 1s state and negligible in all the other states, i.e. only for the lines of the K-series. In practice, since the energy spacings between two adjacent lines of the KFb complex are much smaller than that between the Ka and the Kb lines (see table I), the spectrum of the KFb complex will display overlaps, depending on the energy resolution of the detector. The Ka line is therefore the most important line in determining the level shift and the width of the 1s level. The shift e and the width G of the 1s state of kaonic hydrogen are related in a fairly model- independent way to the real and imaginary part of the s-wave scattering length aK2 p : i 2 1 4 3 2 2 4 2 1 (1) e G 2a m aK p 412aK p eV fm , 2 with m reduced mass and a fine-structure constant. This expression is known as the Deser-Trueman formula [1]. If one neglects the mass difference between the K2 p and 0 K n systems and the Coulomb correction, aK2 p is simply the average of the scattering 4 4 lengths a0 (I 0) and a1 (I 1): 1 2 4 1 (2) aK p (a0 a1). 2 2. – Experiments on kaonic hydrogen Three measurements of kaonic hydrogen X-rays were carried out at CERN and at Rutherford in the late 70’s through the early 80’s [2-4]. Recently, a fourth measure- ment has been performed at KEK [5]. In the three old measurements a liquid hydrogen target and Si(Li) detectors were used. Davies et al.[2] observed a 2s peak at 6 6.52 0.06 keV, which they attributed to the Ka line. Izycki et al. [3] observed a weak pattern of 3 lines at 6.9660.09, 7.9960.07 and 8.6460.10 keV, with significance 2s, 3s and 2s, which they assigned to the 2pK, 3pK and 4pK1s transitions. Bird et al. [4] saw a similar series of three lines with significance s, 3s and 0.5 s, respectively. All the three spectra suffered from large background and low statistics: X-ray signals were very difficult to identify, being strongly attenuated due to the Stark effect present in the liquid hydrogen target. A common feature, notwithstanding the extremely scarce quality of the data, was however apparent: the sign of the shift, and, consequently, that of the real part of the K2 p scattering length, was positive (attractive strong interaction). This was in striking contradiction with the results of the analyses of 1350 C. GUARALDO, M. BRAGADIREANU, M. ILIESCU, ETC. TABLE II. – The "kaonic hydrogen puzzle" and its solution. 2 Method Author aK p (fm) K2 p scattering Sakitt et al. (1965) (20.91 6 0.05) 1 i(0.48 6 0.03) analyses Kim et al. (1967) (20.87 6 0.04) 1 i(0.69 6 0.03) von Hippel et al. (1968) (20.89 6 0.02) 1 i(0.62 6 0.02) Martin and Ross (1970) (20.89 6 0.03) 1 i(0.66 6 0.03) Martin et al. (1981) (20.66 6 0.05) 1 i(0.64 6 0.04) 6 1 10.28 Kaonic-hydrogen Davies et al. [2] (0.10 0.14) i(0.0020.00) X-ray Izycki et al. [3] (0.65 6 0.19) 1 i(0.68 6 0.31) 6 1 10.27 measurements Bird et al.
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